Research techniques of prognostics for gas turbines and diesel engines have advanced in recent years. An analysis of trends in these techniques would benefit researchers assessing growth in the field and planning future research efforts. Prognostics research techniques were identified in 1,734 published papers dated 1997-2016 from both the Prognostics and Health Management (PHM) Society and papers identified by CiteSeerx that were published at venues other than the PHM Society. In order to categorize papers by research technique, a taxonomy of prognostics was created. Additionally, the papers were categorized into two topics: gas turbines and diesel engines. In a large proportion of papers, trends in research techniques of prognostics for gas turbines and diesel engines reflected improvements in the speed of multi-core computer processors, the development of optimized learning methods, and the availability of large training sets. The variety of prognostics research techniques that were identified in this review demonstrated the growth in prognostics research and increased use of this knowledge in the field. This systematic analysis of trends in research techniques of prognostics for gas turbines and diesel engines is useful to assess growth and utilization of knowledge in the larger field, and to provide a rationale (i.e., strategy, basis, structure) for planning the most effective use of limited research resources and funding.